An army post with 1800 men has provision of food for 50 days. After 10 days,…

Concept

In ration/provision problems, total food is measured in man-days: total man-days = (number of men) × (number of days the food lasts). This quantity is conserved — the man-days consumed plus the man-days still available always equal the original total, regardless of how the men or days change.

Application

1. Original total food = 1800 men × 50 days = 90000 man-days.

2. Food eaten in the first 10 days by all 1800 men = 1800 × 10 = 18000 man-days.

3. Food left after 10 days = 90000 − 18000 = 72000 man-days.

4. Let the number of remaining men be R. This leftover food must last the next 50 days, so R × 50 = 72000, giving R = 1440 men.

5. Men who went back = original − remaining = 1800 − 1440 = 360.

Cross-check

Verify by the other route: the untouched 40 days of the original schedule hold 1800 × 40 = 72000 man-days, which matches the leftover food. Spread over 50 days that is 72000 ÷ 50 = 1440 men, so 360 men must have left — consistent with the man-days balance.